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How to Make a Polyhedron in GeoGebra

You can use GeoGebra to draw polyhedra:

GeoGebra Instruction 1

Drawing a Tetrahedron

1.
Open Algebra View and Graphics View under GeoGebra icon View in GeoGebra icon Menu.
2.
Select the tool Regular polygon GeoGebra icon, which is the fifth item in the Toolbar and the second tool from that list.
3.
Draw an equilateral triangle by clicking on two points in Graphics View. These will be two of the vertices of the triangle. When GeoGebra asks you how many vertices you want, type 3.
4.
Open 3D Graphics and close Graphics View under GeoGebra icon View in GeoGebra icon Menu.
5.
Click on an empty space in 3D Graphics to update Toolbar with new tools. Select the tool Tetrahedron GeoGebra icon from the ninth item in the Toolbar (Pyramid GeoGebra icon) and the seventh tool from that list.
6.
Click on the triangle you made in Step 4.

The tetrahedron will now appear in 3D Graphics. The volume of the tetrahedron will appear in Algebra View.

GeoGebra Instruction 2

Drawing an Octahedron

1.
Open Algebra View and Graphics View under GeoGebra icon View in GeoGebra icon Menu.
2.
Select the tool Regular polygon GeoGebra icon, which is the fifth item in the Toolbar and the second tool from that list.
3.
Draw an equilateral triangle by clicking on two points in Graphics View. This will be two of the vertices of the triangle. When GeoGebra asks you how many vertices you want, type 3. Pay attention to the name of the triangle, since it will be used in a later step. GeoGebra will call it poly1 in a new file.
4.
Open 3D Graphics and close Graphics View under GeoGebra icon View in GeoGebra icon Menu.
5.
In new row in Algebra View, type in

Octahedron

and select

Octahedron(<Equilateral Triangle>)

among the options that appear. Replace <Equilateral Triangle> with the name of your triangle from Step 3 in Item 6.

The octahedron will now appear in 3D Graphics. The volume of the octahedron will appear in Algebra View.

GeoGebra Instruction 3

Drawing an Icosahedron

1.
Follow Steps 1–4 in Item 5.
2.
In a new row in Algebra View, type in

Icosahedron

and select

Icosahedron(<Equilateral Triangle>)

among the options that appear. Replace <Equilateral Triangle> with the name of your triangle from Step 3 in Item 5.

The icosahedron will now appear in 3D Graphics. The volume of the icosahedron will appear in Algebra View.

GeoGebra Instruction 4

Drawing a Cube

1.
Open Algebra View and Graphics View under GeoGebra icon View in GeoGebra icon Menu.
2.
Select the tool Regular polygon GeoGebra icon, which is the fifth item in the Toolbar and the second tool from that list.
3.
Draw a square by clicking on two points in Graphics View. These will be two of the vertices of the square. When GeoGebra asks you how many vertices you want, type 4.
4.
Open 3D Graphics and close Graphics View under GeoGebra icon View in GeoGebra icon Menu.
5.
Click on an empty space in 3D Graphics to update Toolbar with new tools. Select the tool Cube GeoGebra icon from the ninth item in the Toolbar (Pyramid GeoGebra icon) and the eighth tool from that list.
6.
Click on the square you made in Step 3.

The cube will now appear in 3D Graphics. The volume of the cube will appear in Algebra View.

GeoGebra Instruction 5

Drawing a Dodecahedron

1.
Open Algebra View and Graphics View under GeoGebra icon View in GeoGebra icon Menu.
2.
Select the tool Regular polygon GeoGebra icon, which is the fifth item in the Toolbar and the second tool from that list.
3.
Draw a regular pentagon by clicking on two points in Graphics View. These will be two of the vertices of the pentagon. When GeoGebra asks you how many vertices you want, type 5. Pay attention to the name of the pentagon, since it will be used in a later step. GeoGebra will call it poly1 in a new file.
4.
Open 3D Graphics and close Graphics View under GeoGebra icon View in GeoGebra icon Menu.
5.
In a new row in Algebra View, type in

Dodecahedron

and select

Dodecahedron(<Regular Pentagon>)

among the options that appear. Replace <Regular Pentagon> with the name of the pentagon you made in Step 3.

The dodecahedron will appear in 3D Graphics. The volume of the dodecahedron will appear in Algebra View.

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How to Draw Prisms in GeoGebra